1393
J . Phys. Chem. 1991, 95, 1393-1396
Analysis of the Low-Field Microwave Absorption Line Shape Differences in YBa,Cu,O, and Bi,Sr,CaCu,O, Superconductors Jerzy T. Masiakowski,+ Micky Puri, and Larry Kevan* Department of Chemistry and Texas Center f o r Superconductivity, University of Houston, Houston, Texas 77204-5641 (Received: August 14, 1990)
The field-dependentlow-field microwave absorption for YBa,Cu,O, (1 23) and Bi2Sr2CaCu20x(2212) superconducting powders and a 2212 crystal was investigated as a function of temperature and magnetic field modulation amplitude. The 2212 samples do not show a significant magnetic field sweep hysteresis while the I23 samples show a hysteresis strongly dependent on temperature and modulation amplitude. The microwave absorption line shapes for all samples, including the signals exhibiting strong hysteretic behavior, can be well simulated by a model for the microwave loss in intergranular Josephson junctions involving boundary and microwave-induced currents. The calculations allow an estimate of the average Josephson junction length to be about half the average grain size observed by scanning electron microscopy. Interpretation based on the assumptions in the line shape model indicates that the Josephson junctions are more weakly coupled in 221 2 than in 123 superconductors.
Introduction
One of the many interesting features of the high-temperature oxide superconductors is the nonresonant, low-field microwave absorption (LFMA) observed below the superconducting transition temperature, T,. Although the absorption has been attributed to the damped motion of trapped magnetic flux at intergranular Josephson junctions, the mechanism is not well understood. Recently, a more specific model for the microwave loss mechanism was proposed and used to calculate the LFMA line shape in YBa2Cu30, powder by Dulcic et al.’ They showed calculated line shapes for a powder sample in agreement with experiment where significant hysteresis was present. We showed that the model can also account for the more complex line shape in a Bi2Sr2CaCu20, crystal at 76 K under the assumption that two major types of Josephson junctions are present.2 In this paper we explore the applicability of the model for explaining the LFMA line shapes of powder samples under different experimental conditions which control the degree of hysteresis. The model gives new insight into the differences between the LFMA response in the YBa2Cu30, and Bi2Sr2CaCu20, systems.
Theory Dulcic et al. consider the boundary current, Io, induced on the surface of the sample by the magnetic field sweep, superimposed on which are microwave magnetic field induced, Imw cos (wmwt), and modulation magnetic field induced, I M cos ( w M t ) currents, , where w,, is the microwave frequency and wM is the magnetic field modulation frequency. The boundary current Io is limited by the weakest Josephson junction links on the surface, so that for any single junction the critical current I , > Io. This model gives the following equation for the LFMA signal shape. S=
((1 /2)Imw2R)’/2
parameter q is a junction coupling parameter proportional to I,2 cos2 cpo. The field dependence of the signal shape is determined by the critical current I,(H,T) = I,(O,T) F(H). For a single, small Josephson junction F ( H ) is given by the diffraction formula I[sin ( r H / H o ) ] / ( 7 r H / H o ) lfor tunneling supercurrent.3 Ho is the magnetic field value for which the junction contains only one quantum of magnetic flux, The effect of a magnetic field on the junction causes cpo to vary, and cpo = 27r corresponds to an intergral number of flux quanta. Thus, cpo = 27r corresponds to H = nHo and the tunneling current drops to zero since Io = I, sin 27r. The Ho value is characteristic for a particular junction because it is related to the junction size and the superconducting material by the relation4ss Ho = 9o/L(2X + t ) (2) where L is the junction length, h is the London penetration depth, and t is the junction thickness. For powder samples there is a broad distribution of Ho characterizing different junction types and sizes. This distribution is approximated’ by using the envelope of the maxima given by the diffraction formula. This gives a smooth line shape as observed experimentally instead of the discontinuous shape given by the diffraction formula for a single HO. The reversible term of the line shape equation ( I ) is proportional to the expression
SAH)
F(H)[I + ~ O F ~ ( H ) I - ” ~ I - ~ F ( H ) / ~ (H3 )J
The qo parameter is defined by q = q 0 P ( H ) and contains information about the temperature dependence because qo = I:(0,T).
The irreversible term responsible for hysteresis is proportional to the expression
X
((1 / R ) ( h / 4 7 r e ) ~ m w ) ~
-2 -
H M + I M sin
(1 +I;),,,[
cpo
1
cos WMt ( I )
This equation consists of two terms. The first term is independent of the direction of the magnetic field sweep and is called the reversible term. The second term changes sign when the field sweep is reversed because cpo -cpo and is called the hysteretic term. The symbols h and e are Planck’s constant and the electronic charge. The other symbols are defined as follows. HM is the amplitude of the magnetic field modulation, R is the resistance of the junction when nonsuperconducting, and cpo is the equilibrium phase difference of the wave functions of the superconducting electrons across the junction defined by Io = I , sin cpo. The
’
Permanent address: Department of Physics, Adam Mickiewicz University, PL-60780 Poznan, Poland.
0022-3654/91/2095-1393%02.50/0
The modulated microwave absorption signal is the sum (for forward magnetic field sweep) and the difference (for backward magnetic field sweep) of the reversible and hysteretic terms since the hysteretic term changes sign when the field sweep is reversed. Figure 1 shows contributions of the reversible and hysteretic terms to the microwave absorption line shape for three different temperatures in the range of 0 K to T, (qo 0 corresponds to T T,). An increase ‘in qo above 100 does not significantly
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-
( I ) Dulcic, A.; Rakvin, B.; Pozek, M. Europhys. Lett. 1989, 10, 593. (2) Masiakowski, J. T.; Puri, M.; Cuvier, S.; Romanelli, M.; Schwartz, R. N.; Kimura, H.; Kevan, L. Physicu C 1990, 166, 140. (3) Josephson, B. D. Rev. Mod. Phys. 1964, 36, 216. (4) Barone, A.; Paterno, G. In Physics and Applications of the Josephson Eflect; Wiley: New York, 1982; p 74. ( 5 ) Weihnacht, M. Phys. Status Solidi 1969, 32, K169.
0 199 1 American Chemical Society
1394 The Journal of Physical Chemistry, Vol. 95, No. 3, 1991
Masiakowski et al.
I
I
25 0
I
225 H (Gauss)
I
-3
0
I
J
3
6
H/~,
Figure 1. Reversible (solid line) and hysteretic (dashed line) contributions to the LFMA line shape for three different qo values covering the temperature range from 0 K to T,. The arrows on the dashed lines indicate thc magnetic field sweep direction. change the calculated line shape: thus for qo > 100 we can assume that effectively T = 0. The observed line shape depends on the ratio of the amplitudes of these contributions. The modulation amplitude has different influences on the two terms of the model. The sweep-independent, reversible term grows linearly with the modulation amplitude, eventually saturating in high modulation amplitudes. The hysteretic term is derived assuming lM
